I had also faced the same error in the recent past.
This error usually occurs due to the multiple installations of mysql.
You need to Run the below command :
ps -A|grep mysql
Kill your process by using below command :
sudo pkill mysql
And after that you need to run the below command :
ps -A|grep mysqld
Also Kill your process by running below command :
sudo pkill mysqld
Now you are completely set just you need to run the below commands :
service mysql restart
mysql -u root -p
That’s it you are all set now !! Have a very well working Mysql again !!